Elliott is appealing the fine.
Elliott was the first offensive player to be flagged for that penalty this season.
The rule, approved last spring, prohibits players from lowering their helmets to initiate contact with an opponent. League officials said at the time that it would apply to all players at every position, and noted specifically that running backs who lowered their heads to bowl over defenders would be called. But through the first 13 weeks of the season, only defensive or special-teams players had been penalized.
The play occurred with 11 minutes, 32 seconds remaining in regulation of the Cowboys' overtime victory Sunday against the visiting Eagles. Elliott lowered his head and hit Graham at the end of a 12-yard reception.
It's the second time in four weeks Elliott has been fined. He was fined $13,369 for unsportsmanlike conduct for donating $21 into the Salvation Army kettle after a touchdown against Washington.
Information from ESPN's Kevin Seifert was used in this report.